Math 160, Chapter 13, Collecting Statistical Data
Definition 1.1. a) Data is information in numerical form.
b) The population is the group of individuals or objects that is being studied.
c) The N-value of the population is the total number of individuals/objects in
the population.
d) A parameter is a quantity that one is trying to measure in a statistical study.
e) A sample is the collection of individuals/objects drawn from the population
that is used for estimating a parameter.
Definition 1.2. a) The sampling method is the method used to select the sample: simple random sampling, stratified random sampling, convenience sampling,
quota sampling.
b) Simple random sampling is when everyone in the population has the same
chance of being selected for the sample.
c) In stratified random sampling one first divides the population into strata
(different groups) and then takes a random sampling from each of the groups.
d) In convenience sampling the selection is based on what the easiest or
cheapest way is to select individuals for the sample.
e) Quota sampling is a systematic way of making a representative sampling
from the population.
f) The sampling frame is the subset of the population from which the sample
is drawn.
Definition 1.3. a) A statistic is an estimate for the parameter based on a given
sample.
b) The sampling error is the difference between the actual value of the parameter and the estimate obtained from the sample statistic.
c) Statistics is the science of gathering, organizing and understanding data.
Definition 1.4. Common Faults with sampling methods.
a) Selection bias occurs when the sample method has a built in tendency to
exclude a particular group within the population.
b) Non-response bias occurs when the percentage of respondents from the
intended sample is very low.
Definition 1.5. The capture-recapture method is a method for estimating the
size of a population using the following steps.
1. First “capture” (choose) a random sample from the population and mark the
individuals in the sample.
2. Place the captured sample back in the population, and give the population
time to become randomized again.
3. “Recapture” (choose) a new random sample from the population.
4. Count the number of marked individuals in the recaptured sample.
5. Estimation: N ≈ n1kn2 , where N = population, n1 =first sample size,
n2 =second sample size, k =number of marked individuals in the second sample.
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Definition 1.6. a) A clinical study is a study used to determine whether a certain
variable can cause a certain effect.
b) In a controlled study the subjects are divided into two groups, the treatment group and the control group.
c) A placebo is a make-believe form a treatment (fake pill for example) given
to the control group that is indistinguishable from the real treatment.
d) The placebo effect is when a positive result occurs because an individual
believes he/she is receiving the real treatment, even though he/she is actually receiving a placebo.
e) A blind study is a study in which members do not know whether they are
in the control group or the treatment group.
f) A double blind study is a study in which neither the subjects nor the
scientists conducting the study know who is in the treatment group and who is in
the control group.